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A229392 T(n,k)=Number of nXk 0..3 arrays of the sum of the corresponding element, the element to the east and the element to the south in a larger (n+1)X(k+1) 0..1 array 8
4, 14, 14, 48, 128, 48, 164, 1064, 1064, 164, 560, 8592, 19124, 8592, 560, 1912, 68672, 319340, 319340, 68672, 1912, 6528, 546752, 5212236, 10624396, 5212236, 546752, 6528, 22288, 4346752, 84210828, 345788172, 345788172, 84210828, 4346752, 22288 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
.....4........14...........48.............164................560
....14.......128.........1064............8592..............68672
....48......1064........19124..........319340............5212236
...164......8592.......319340........10624396..........345788172
...560.....68672......5212236.......345788172........22494002188
..1912....546752.....84210828.....11156280332......1451228983308
..6528...4346752...1353901580....358453456908.....93250181644300
.22288..34537984..21715025932..11493734735884...5979900142878732
.76096.274370048.347864379404.368171037655052.383094040360124428
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -2*a(n-2)
k=2: a(n) = 12*a(n-1) -36*a(n-2) +32*a(n-3) -16*a(n-4)
k=3: a(n) = 25*a(n-1) -152*a(n-2) +144*a(n-3) -368*a(n-4) +1888*a(n-5) -1536*a(n-6) for n>9
k=4: a(n) = 49*a(n-1) -560*a(n-2) +544*a(n-3) -1568*a(n-4) +17920*a(n-5) -16384*a(n-6) for n>9
k=5: a(n) = 101*a(n-1) -2532*a(n-2) +10624*a(n-3) -8192*a(n-4) for n>7
k=6: a(n) = 193*a(n-1) -8384*a(n-2) +8320*a(n-3) -24704*a(n-4) +1073152*a(n-5) -1048576*a(n-6) for n>9
k=7: a(n) = 385*a(n-1) -33152*a(n-2) +33024*a(n-3) -98560*a(n-4) +8486912*a(n-5) -8388608*a(n-6) for n>9
k=8: a(n) = 777*a(n-1) -137992*a(n-2) +1185792*a(n-3) -1048576*a(n-4) for n>7
k=9: a(n) = 1537*a(n-1) -525824*a(n-2) +525312*a(n-3) -1573888*a(n-4) +538443776*a(n-5) -536870912*a(n-6) for n>9
k=10: a(n) = 3073*a(n-1) -2100224*a(n-2) +2099200*a(n-3) -6293504*a(n-4) +4301258752*a(n-5) -4294967296*a(n-6) for n>9
k=11: a(n) = 6161*a(n-1) -8493072*a(n-2) +142704640*a(n-3) -134217728*a(n-4) for n>7
EXAMPLE
Some solutions for n=3 k=4
..1..1..0..1....1..1..1..3....0..1..1..2....0..1..2..3....0..0..2..1
..0..0..1..0....3..2..1..2....2..1..0..0....2..2..2..2....0..1..2..1
..1..2..2..1....3..1..2..3....2..1..0..1....2..0..2..3....0..1..2..3
CROSSREFS
Column 1 is A007070
Sequence in context: A168420 A189814 A200553 * A229320 A127302 A204541
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Sep 21 2013
STATUS
approved

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Last modified April 23 10:13 EDT 2024. Contains 371905 sequences. (Running on oeis4.)